In zita-rev1, the damping filter for each delay line consists
of a low-shelf filter
[449],4.19in series with a unique first-order lowpass filter that sets
the high-frequency to be half that of the middle-band at a
particular frequency (specified as ``HF Damping'' in the GUI).
Since the filter is constrained to be a lowpass,
for , i.e., the decay time gets
shorter at higher frequencies.

Viewing the resulting damping filter
as a
three-band filter bank (§3.7.5), let and denote the
desired band gains at dc and ``middle frequencies'',
respectively.4.20 Then the low shelf may be set for a
desired dc-gain of , and its input (or output) signal
multiplied by to obtain the resulting filter

where specifies (in Hz) the crossover point between ``low'' and
``middle'' frequencies, and denotes the sampling interval as
usual.

The lowpass filter is also first order, and to provide half
the middle-band at the beginning of the ``high'' band, the
lowpass should ``break'' to a gain of at the ``HF Damping''
frequency specified in the GUI. A unity-dc-gain one-pole
lowpass has the form [449]

where the pole must be found to give a gain of at frequency :

Squaring and normalizing yields a quadratic equation of the form
. Solving for using the quadratic formula
yields

where

and the unstable solution
is discarded.
To ensure , the GUI must limit the middle-band to
finite values. (The upper limit is presently seconds for both low
and middle frequencies.)